Pulse-shaping filter specification object
D = fdesign.pulseshaping
D = fdesign.pulseshaping(sps)
D = fdesign.pulseshaping(sps,shape)
d = fdesign.pulseshaping(sps,shape,spec,value1,value2,...)
d = fdesign.pulseshaping(...,fs)
d = fdesign.pulseshaping(...,magunits)
D = fdesign.pulseshaping constructs a specification object D, which can be used to design a minimum-order raised cosine filter object with a default stop band attenuation of 60dB and a rolloff factor of 0.25.
D = fdesign.pulseshaping(sps) constructs a minimum-order raised cosine filter specification object d with a positive integer-valued oversampling factor, SamplesPerSymbol .
D = fdesign.pulseshaping(sps,shape) constructs d where shape specifies the PulseShape property. Valid entries for shape are:
'Square Root Raised Cosine'
d = fdesign.pulseshaping(sps,shape,spec,value1,value2,...) constructs d where spec defines the Specification properties. The string entries for spec specify various properties of the filter, including the order and frequency response. Valid entries for spec depend upon the shape property. For 'Raised Cosine' and 'Square Root Raised Cosine' filters, the valid entries for spec are:
'Ast,Beta' (minimum order; default)
The string entries are defined as follows:
Ast —stopband attenuation (in dB). The default stopband attenuation for a raised cosine filter is 60 dB. The default stopband attenuation for a square root raised cosine filter is 30 dB. If Ast is specified, the minimum-order filter is returned.
Beta —rolloff factor expressed as a real-valued scalar ranging from 0 to 1. Smaller rolloff factors result in steeper transitions between the passband and stopband of the filter.
Nsym —filter order in symbols. The length of the impulse response is given by Nsym*SamplesPerSymbol+1. The product Nsym*SamplesPerSymbol must be even.
N —filter order (must be even). The length of the impulse response is N+1.
If the shape property is specified as 'Gaussian', the valid entries for spec are:
The string entries are defined as follows:
Nsym—filter order in symbols. Nsym defaults to 6. The length of the filter impulse response is Nsym*SamplesPerSymbol+1. The product Nsym*SamplesPerSymbol must be even.
BT —the 3–dB bandwidth-symbol time product. BT is a positive real-valued scalar, which defaults to 0.3. Larger values of BT produce a narrower pulse width in time with poorer concentration of energy in the frequency domain.
d = fdesign.pulseshaping(...,fs) specifies the sampling frequency of the signal to be filtered. fs must be specified as a scalar trailing the other numerical values provided. For this case, fs is assumed to be in Hz and is used for analysis and visualization.
linear — specify the magnitude in linear units
dB — specify the magnitude in dB (decibels)
squared — specify the magnitude in power units
When you omit the magunits argument, fdesign assumes that all magnitudes are in decibels. Note that fdesign stores all magnitude specifications in decibels (converting to decibels when necessary) regardless of how you specify the magnitudes.
After creating the specification object d, you can use the design function to create a filter object such as h in the following example:
d = fdesign.pulseshaping(8,'Raised Cosine','Nsym,Beta',6,0.25); h = design(d);
Normally, the Specification property of the specification object also determines which design methods you can use when you create the filter object. Currently, regardless of the Specification property, the design function uses the window design method with all fdesign.pulseshaping specification objects. The window method creates an FIR filter with a windowed impulse response.
Pulse-shaping can be used to change the waveform of transmitted pulses so the signal bandwidth matches that of the communication channel. This helps to reduce distortion and intersymbol interference (ISI).
This example shows how to design a minimum-order raised cosine filter that provides a stop band attenuation of 60 dB, rolloff factor of 0.50, and 8 samples per symbol.
h = fdesign.pulseshaping(8,'Raised Cosine','Ast,Beta',60,0.50); Hd = design(h); fvtool(Hd)
This code generates the following figure.
This example shows how to design a raised cosine filter that spans 8 symbol durations (i.e., of order 8 symbols), has a rolloff factor of 0.50, and oversampling factor of 10.
h = fdesign.pulseshaping(10,'Raised Cosine','Nsym,Beta',8,0.50); Hd = design(h); fvtool(Hd, 'impulse')
This example shows how to design a square root raised cosine filter of order 42, rolloff factor of 0.25, and 10 samples per symbol.
h = fdesign.pulseshaping(10,'Square Root Raised Cosine','N,Beta',42); Hd = design(h); fvtool(Hd, 'impulse')
The following example demonstrates how to create a Gaussian pulse-shaping filter with an oversampling factor (sps) of 10, a bandwidth-time symbol product of 0.2, and 8 symbol periods. The sampling frequency is specified as 10 kHz.